function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%


%sigmoid = (1/1+exp(-theta' * X'))';

%J = log(sigmoid) .* -y
%J = 1./m * sum(-y.*log(sigmoid(X * theta)) - (1 - y') * log(1 - sigmoid(X * theta)));
 J = 1./m *    (-y'*log(sigmoid(X*theta)) - ( 1 - y' ) * log (1 - sigmoid( X * theta)))

grad = 1./m * X' * (sigmoid(X * theta) - y);
%J = log((sigmoid)) .* -y
%J = sum((log(sigmoid) .* -y) );
%J = - log(1 - sigmoid) .* (1-y)
%J = log((1/1+exp(-theta' * X'))') .* -y







% =============================================================

end
